The idea that an agent could not do otherwise in exactly the same circumstances is considered a problem facing both libertarians and determinists. Classical mechanical determinism is "information preserving." And so is the time evolution of the Schrödinger equation in quantum mechanics.

Information philosophy has a particular importance for this question, because it can be asked whether exactly the same information could ever be present at two different locations in the universe of space and time.

Surprisingly, in the classical mechanical deterministic universe all moments of time contain exactly the same information, since complete knowledge of the universe at any time implies the exact situation at all other times, past and present (cf., Laplace's Demon).

Perhaps equally surprising is the fact that in our expanding universe where information is being destroyed with the increase in entropy, and simultaneously new information is being created - sadly somewhat less than the increase in disorder - we can say that the exact same circumstances never occur.

This dramatic difference is one of the most outstanding disproofs of the metaphysical idea of physical determinism, which is seen to be an illusion.

That the exact same circumstances never occur is nowhere more clear than in systems that clearly store the increased information and so exhibit a record of the change in the universe. Astrophysical objects show signs of their evolution. The geological record of the earth's surface displays a rich past. Most living organisms have encoded traces of their lives. And of course human beings carry a part of their past in their memories.

So, like many philosophical problems, the idea of "exactly the same circumstances" reduces to the practical problem of being in very similar circumstances, which is still an interesting question.

Libertarians who think they require a sort of extreme "metaphysical freedom" have argued for what some call a "plurality condition" or a "dual rational power." They want a "rational" decision to be able to do something different in exactly the same circumstances. This is only possible if genuinely new alternative possibilities are generated for consideration by the rational and adequately determined will.

Imagine that I first walk through Divinity Avenue, and then imagine that the powers governing the universe annihilate ten minutes of time with all that it contained, and set me back at the door of this hall just as I was before the choice was made. Imagine then that, everything else being the same, I now make a different choice and traverse Oxford Street. You, as passive spectators, look on and see the two alternative universes,--one of them with me walking through Divinity Avenue in it, the other with the same me walking through Oxford Street. Now, if you are determinists you believe one of these universes to have been from eternity impossible: you believe it to have been impossible because of the intrinsic irrationality or accidentality somewhere involved in it. But looking outwardly at these universes, can you say which is the impossible and accidental one, and which the rational and necessary one? I doubt if the most ironclad determinist among you could have the slightest glimmer of light on this point. In other words, either universe after the fact and once there would, to our means of observation and understanding, appear just as rational as the other.
(The Will to Believe, 1897, p.155)

Peter van Inwagen wrote in his 2000 essay "Free Will Is Still A Mystery" about a thought experiment where God reset the circumstances to be the same, and he imagined the outcome of free decisions which have intrinsic unpredictability because they are indeterministic. Van Inwagen argued that there would be a statistical distribution of outcomes, as the agent did different things following the distribution of indeterministic causes.

Now let us suppose that God a thousand times caused the universe to revert to exactly the state it was in at t1 (and let us suppose that we are somehow suitably placed, metaphysically speaking, to observe the whole sequence of "replays"). What would have happened? What should we expect to observe? Well, again, we can't say what would have happened, but we can say what would probably have happened: sometimes Alice would have lied and sometimes she would have told the truth. As the number of "replays" increases, we observers shall — almost certainly — observe the ratio of the outcome "truth" to the outcome "lie" settling down to, converging on, some value. We may, for example, observe that, after a fairly large number of replays, Alice lies in thirty percent of the replays and tells the truth in seventy percent of them—and that the figures 'thirty percent' and 'seventy percent' become more and more accurate as the number of replays increases. But let us imagine the simplest case: we observe that Alice tells the truth in about half the replays and lies in about half the replays. If, after one hundred replays, Alice has told the truth fifty-three times and has lied forty-eight times, we'd begin strongly to suspect that the figures after a thousand replays would look something like this: Alice has told the truth four hundred and ninety-three times and has lied five hundred and eight times. Let us suppose that these are indeed the figures after a thousand [1001] replays. Is it not true that as we watch the number of replays increase we shall become convinced that what will happen in the next replay is a matter of chance. ("Free Will Remains a Mystery," in Philosophical Perspectives, vol. 14, 2000, p.14)

Although this is consistent with those who think that indeterminism directly affects our actions, it is not at all what our Cogito model suggests. Indeterminism affects only the alternative possibilities available to the agent for choice. These alternative possibilities are likely to vary from circumstance to circumstance, making the agent unpredictable.

But assuming for the sake of argument that identical alternative possibilities came to mind, the Cogito model predicts that the agent will make the same determination based on character and values. Those libertarians who want something different to happen have an antipathy to determination like that William James found in determinists with their antipathy to chance.

We can make a quantitative comparison of the outcome of 1000 thought experiments (or "instant replays" by God as van Inwagen imagines) that shows how the indeterminism in the Cogito Model is limited to generating alternative possibilities for action.

Van Inwagen's results after 1000 experiments are approximately 500 lies and 500 times when Alice tells the truth.

Robert Kane is well aware of the problem that chance reduces moral responsibility, especially in his sense of Ultimate Responsibility (UR).

In order to keep some randomness but add rationality, Kane says perhaps only some small percentage of decisions will be random, thus breaking the deterministic causal chain, but keeping most decisions predictable. Laura Ekstrom and others follow Kane with some indeterminism in the decision.

Let’s say randomness enters Kane’s decisions only ten percent of the time. The other ninety percent of the time, determinism is at work. In those cases, presumably Alice tells the truth. Then Alice’s 500 random lies in van Inwagen’s first example would become only 50.

But this in no way explains moral responsibility for those few cases.

Compare the Information Philosophy Cogito model, which agrees with compatibilism/determinism except in cases where something genuinely new and valuable emerges as a consequence of randomness.

In our two-stage model, we have first “free” – random possibilities, then “will” – adequately determined evaluation of options and selection of the "best" option.

Alice’s random generation of alternative possibilities will include 50 percent of options that are truth-telling, and 50 percent lies.

Alice’s adequately determined will evaluates these possibilities based on her character, values, and current desires.

In the Cogito model, she will almost certainly tell the truth. So it predicts almost the same outcome as a compatibilist/determinist model.

The Cogito model is not identical, however, since it can generate new alternatives.

It is possible that among the genuinely new alternative possibilities generated, there will be some that determinism could not have produced.

It may be that Alice will find one of these options consistent with her character, values, desires, and the current situation she is in. One might include a pragmatic lie, to stay with van Inwagen’s example.

In a more positive example, it may include a creative new idea that information-preserving determinism could not produce.

Alice’s thinking might bring new information into the universe. And she can legitimately accept praise (or blame) for that new action or thought that originates with her.

To summarize the results:

Van Inwagen

Kane

Cogito

Compatiblism

Alice tells truth

500

950

1000*

1000

Alice lies

500

50

0*

0

* (Alice tells the truth unless a good reason emerges from her free deliberations in the Cogito Model, in which case, to stay with van Inwagen's actions, she might tell a pragmatic lie.)

Let’s consider the Moral Luck criticism of actions that have a random component in their source.